No. You use the the second conditional to talk about present or future possibilities that are either impossible or probably not going to be true. You use the third conditional to talk about something from the past that did not, or could not happen.
Second conditional uses the past simple followed by 'would' and the infinitive. Because it uses the infinitive it cannot express a past possibility, although the condition on which the future possibility hangs may itself involve the past.
Your quote is not a complete example - it is only the condition.
A complete example would be:
- If I had the brains I'd invent something greatpaid more attention at school I could get a better job.
The condition is something from the past ('brains' or knowledge that you didn't gain), but the possibility that hangs on it is a future intention (to invent something great)you could have done now or in the future.
The third conditional uses the past tense and not the infinitive. Both the condition and the event are in the past:
- If I had had the brainsopportunity I would have inventedgone something greatto college.